God necessarily exists
Formal Statement
God, or substance consisting of infinite attributes each expressing eternal and infinite essentiality, necessarily exists. God is substance (Def.6); existence belongs to the nature of substance (P7); therefore God exists. Furthermore, as absolutely infinite, God's essence involves no negation and so no reason for non-existence can be found either in God's nature or outside it.
In Plain Language
This is the ontological peak of the system. Everything has been building to this. God is substance (that was the definition), and substance necessarily exists (that was P7). So God necessarily exists. Spinoza offers multiple proofs, but the cleanest one is simply: if God did not exist, God's essence would not involve existence — but substance's essence does involve existence, and God is substance. The denial is self-contradictory. Notice that this "God" is not being proved as a designer or a person, but as the necessarily existing, absolutely infinite substance.
Why This Follows
God is defined as absolutely infinite substance (gs-04). P7 (gs-09) proved that existence belongs to the nature of substance. P8 (gs-10) proved that every substance is infinite. So God — the substance with every attribute — necessarily exists. Denying God's existence would mean denying that substance exists, which contradicts P7.
God — absolutely infinite substance — necessarily exists.
Connected Concepts
Does Spinoza's proof work only within his definitional framework, or does it have force independently of it?